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In a parallelepiped \(ABCDEFGH\), we consider the basis \((\Vect{AB}, \Vect{AD}, \Vect{AE})\).
  1. Express the vector \(\Vect{BD}\) in this basis.
  2. Let \(M\) be the midpoint of \([FG]\). Express \(\Vect{AM}\) in this basis.
  3. Give the coordinates of vectors \(\Vect{BD}\) and \(\Vect{AM}\) in the basis \((\Vect{AB}, \Vect{AD}, \Vect{AE})\).

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